This post is a summary and paper skimming on regularization and optimization. So, this post will be keep updating by the time.

Paper List

Regularization

Optimization

Regularizing neural networks by penalizing confident output distributions

  • Conference: ICLR2017

Summary

  • Research Objective
    • To suggest the wide applicable regularizers
  • Proposed Solution
    • Regularizing neural networks by penalizing low entropy output distributions
    • Penalizing low entropy output distributions acts as a strong regularizer in supervised learning.
    • Connect a maximum entropy based confidence penalty to label smoothing through the direction of the KL divergence.
      • When the prior label distribution is uniform, label smoothing is equivalent to adding the KL divergence between the uniform distribution and the network’s predicted distribution to the negative log-likelihood.
      • By reversing the direction of the KL divergence in equation (1), , it recovers the confidence penalty.

Comparision Figure: Distribution of the magnitude of softmax probabilities on the MNIST validation set. A fully-connected, 2-layer, 1024-unit neural network was trained with dropout (left), label smoothing (center), and the confidence penalty (right). Dropout leads to a softmax distribution where probabilities are either 0 or 1. By contrast, both label smoothing and the confidence penalty lead to smoother output distributions, which results in better generalization.

  • Contribution
    • Both label smoothing and the confidence penalty improve state-of-the-art models across benchmarks without modifying existing hyperparameters

Result Figure: Test error (%) for permutation-invariant MNIST.

References